Seminar Knot theory

  Wed 9:15-10:45, RUD25 3.008

Please, register with Moodle for this class.

Literatur: 1. R.H.Crowell and R.H. Fox: Introduction to Knot Theory, Springer 1963  (electronically available in library - you have to use HU-VPN!)
                  2. W.B.R. Lickorish:  An Introduction to Knot Theory, Springer 1997 (electronically available)
                  3. G.Burde, H.Zieschang, M.Heusener: Knots. De Gruyter 2014 (electronically available)
                  4. M.A.Armstrong: Basic Topology. Springer 1983 (electronically available)
                  5. Ch. Livingston: Knot Theory. MAA 1993 (electronically available, also in German)
                  6. V.V. Prasolov, A.B. Sossinsky: Knots, Links, Braids and 3-Manifolds. AMS 1991 (electronically availabe)
                  7. C.C. Adams: On Knots, AMS 2004 (no electronic version available)
                  8. C. Kassel, O.Dodane, V. Turaev: Braid Groups, Springer 2008

There are many more (have a look in the library catalogue).

There is a class on 3-Manifolds by Marc Kegel which is closely related to Knot theory!


05/06    Knots: Definition, Examples (also pathological ones), Links (Lit.: 1., 2., 3.,5.)  Todoulou
05/13    Knot diagrams (definition and existence), Reidemeister moves (including proofs) (1., 2., 3., 5.)  Huneshagen
05/20    Idea of knot invariants. Bridge and unknotting numbers (short discussion). Linking number. Tricolourability (definition, proof of invariance)(internet research) Gerlach
05/27    Knot polynomials (combinatorial definition of Alexander-Conway polynomial (and possibly the Jones polynomial)) Dawid
06/03    Seifert surfaces (Proof of existence). Genus of a knot, additivity under knot sums, prime decompositon of knots (3., 4., 5.) Levinson
06/10    Fundamental group (definition, group axioms), fundamental group of a circle  Mousseau
06/17    Knot group (representation of the fundamental group of the knot complement via knot diagrams) Đukić
06/24    Cyclic coverings and the commutator subgroup of the knot group
07/01    Fibered knots/links El Agami
07/08    Universal cyclic coverings, geometric definition of the Alexander polynomial
07/22   Braid groups, Bureau representation and the Alexander-Conway Polynomial (8.) Maravall

last changes: Thu, July 22,  7:05  p.m.